Atomic radii measurement

Strictly speaking, the size of an atom is a rather nebulous concept The electron cloud surrounding the nucleus does not have a sharp boundary. However, a quantity called the atomic radius can be defined and measured, assuming a spherical atom. Ordinarily, the atomic radius is taken to be one half the distance of closest approach between atoms in an elemental substance (Figure 6.12). 

It is valuable to be able to predict the internuclear distance of atoms within and between molecules, and so there has been much work done in attempting to set up tables of "atomic radii" such that the sum of two will reproduce the internuclear distances. Unfortunately there has been a proliferation of these tables and a bewildering array of terms including bonded, nonbonded, ionic, covalent, metallic, and van der Wauls radii, as well as the vague term atomic radii. This plethora of radii is a reflection of the necessity of specifying what is being measured by an atomic radius. Nevertheless, it is possible to simplify the treatment of atomic radii without causing unwarranted errors. 

The unique ligating behavior of the bridging 2,6-dimethoxyphcnyl ligand with respect to promoting a substantial decrease in the metal atom separation for molybdenum(II) dimers is even more prominent in the case of chromium. The chromium-chromium distance of 1.847(1) A in Cr2(DMP)4 (90) is more than 0.1 A less than the corresponding value in any other chromous dimer yet reported. To compare homonuclear multiple bonds among elements with inherently different atomic radii, Cotton, Koch, and Millar proposed a normalized value for intemuclear distances based on Pauling s atomic radius of the element in question (209). A simple definition of formal shortness as t/(M—M)/2r(M) then follows as a measure of the relative compactness of the attractive interaction (90). The formal shortness ratio of 0.778 for the quadruple bond in... 

It s possible to check the accuracy of atomic radii by making sure that the assigned values are additive. For instance, since the atomic radius of Cl is 99 pm and the atomic radius of C is 77 pm, the distance between Cl and C nuclei when those two atoms are bonded together ought to be roughly 99 pm + 77 pm, or 176 pm. In fact, the measured distance between chlorine and carbon in the chloromethane molecule (CH3CI) is 178 pm, remarkably close to the expected value. 

The physical properties of the elements, such as melting point, boiling point and density are related to the atomic radius of the elements. Also, the atomic radius directly affects the ability of an atom to gain and lose electrons. The atomic radius is practically defined by assuming the shape of the atom as a sphere. The atomic radius is the distance between the nucleus and the outermost electron. But it is impossible to measure the atomic radius by separating the atoms from each other. Atomic Radius within a Group... 

The electron cloud around an atomic nucleus makes the concept of atomic size somewhat imprecise, but it is useful to refer to an atomic radius. One can arbitrarily divide the distance between centers of two bonded atoms to arrive at two radii, based on the crude picture that two bonded atoms are spheres in contact. If the bonding is covalent, the radius is called a covalent radius (see Table 8-2) if it is ionic, the radius is an ionic radius (see Table 9-2). The radius for non-bonded atoms may be defined in terms of the distance of closest non-bonding approach such a measure is called the van der Waals radius. These three concepts of size are illustrated in Figure 7-2. 

The atomic radius is the distance between the nucleus and the outermost electron. Atomic radii are measured in nanometers (10 9 meters). In some fields, atomic radii are measured in a unit known as an angstrom, A (10 10 m or of a nanometer). Hydrogen is the smallest atom, measuring only 0.037 nm or 0.37 A. 

Let us imagine the charges e of the dipole at the positions of the nuclei of the atoms such that s d = fx. The minimum distance for the negative pole of the C—Cl dipole is then determined by the Van der Waals radius of the chlorine atom (Table 17) this is 1.8 A. With the OH group the Van der Waals radius measured from the nucleus of the oxygen atom is 1.40 A. Since the O—H distance is 0.97 A, however, the shortest distance for the (positive) pole to the edge of the Van der Waals sphere is now 0.43 A. 

One effect of lanthanide contraction is that the radius of trivalent yttrium ion (Y +) is measured to be between that of Ho + and Er +, and the atomic radius of yttrium is between neodymium and samarium. This results in the chemical properties of yttrium being very similar to those of lanthanide elements. Yttrium is often found with lanthanide elements in natural minerals. The chemical properties of yttrium may be similar to the lighter or the heavier lanthanide elements in different systems and this depends on the level of covalent character of the chemical bonds in those systems. 

Just as the size of an orbital cannot be specified exactly, neither can the size of an atom. We must make some arbitrary choices to obtain values for atomic radii. These values can be obtained by measuring the distances between atoms in chemical compounds. For example, in the bromine molecule the distance between the two nuclei is known to be 228 pm. The bromine atomic radius... 

Here Rs represents the pore radius measured from the center of the surface atoms, and p is the mean pore density. The radial density profile p(r) is obtained from simulations, while the local viscosity is evaluated using the method of Chung et al. [17], at a density locally averaged over a sphere of radius aj /2 [18]. The radius To in eq. (4) represents... 

The conception of a covalent radius may be tested by considering the hydrides. The covalent radius of the hydrogen atom as measured from molecular hydrogen will be half the bond length, 0 37 A. In Talf/e LIX,... 

By measuring the numbers of alpha particles that were deflected and the angles of deflection, scientists calculated the radius of the nucleus to be less than of the radius of the whole atom. Figure 9 gives you a better idea of these sizes. Even though the radius of an entire atom is more than 10 000 times larger than the radius of its nucleus, an atom is still extremely small. The unit used to express atomic radius is the picometer (pm). One picometer equals 10 m. 

Baddeley et al. [93] also investigated the effect of the adsorbate on the number of visible atoms by measuring the total number of visible Cu and Pd atoms as a function of Cl coverage. They concluded that any effect was negligible and could be discounted in the calculations. This is another advantage of the MEIS approach compared to LEIS. The shadow cone radius varies as so the shadowing effect of H(a), C(a) and 0(a) are all relatively weak and even the effect of Cl(a) can be neglected since it is very unlikely that Cl will sit in a site which is a continuation of the bulk bimetallic lattice. 

The sizes of atoms and ions influence how they interact in chemical compounds. Although atomic radius is not a precisely defined concept, these sizes can be estimated in several ways. If the electron density is known from theory or experiment, a contour surface of fixed electron density can be drawn, as demonstrated in Section 5.1 for one-electron atoms. Alternatively, if the atoms or ions in a crystal are assumed to be in contact with one another, a size can be defined from the measured distances between their centers (this approach is explored in greater detail in Chapter 21). These and other measures of size are reasonably consistent with each other and allow for the tabulation of sets of atomic and ionic radii, many of which are listed in Appendix F. 

We have investigated the validity of (15) for ten different measures of atomic radius [160], R2 ranged from 0.207 to 0.976. This work furthermore supports (14) but suggests that /(Z) is periodic as well as slowly varying. 

Calculations Determining the unit cell type from the measured density and atomic radius of metals in the cubic system the atomic radius of a metal atom is determined from the crystal type and the edge length of a unit cell, which are both obtained by x-ray diffraction (see Major Technique 3 in text). 

---